Decidability results for hybrid automata often exploit subtle properties about dimensionality (number of continuous variables), and interaction between discrete transitions and continuous trajectories of variables. Thus, the decidability results often do not carry over to parallel compositions of hybrid automata, even when there is no communication other than the implicit synchronization of tim...

One of the most important analysis problems of hybrid systems is the reachability problem. State of the art computational tools perform reachability computation for timed automata, multirate automata, and rectangular automata. In this paper, we extend the decidability frontier for classes of linear hybrid systems, which are introduced as hybrid systems with linear vector fields in each discrete...

For an n×n nonnegative matrix P , an isomorphism is obtained between the lattice of initial subsets (of {1, · · · , n}) for P and the lattice of P -invariant faces of the nonnegative orthant R+. Motivated by this isomorphism, we generalize some of the known combinatorial spectral results on a nonnegative matrix that are given in terms of its classes to results for a cone-preserving map on a pol...

The presence of a tight integration between the discrete control (the “cyber”) and the analog environment (the “physical”)—via sensors and actuators over wired or wireless communication networks—is the defining feature of cyberphysical systems. Hence, the functional correctness of a cyberphysical system is crucially dependent not only on the dynamics of the analog physical environment, but also...

This paper addresses questions regarding the decidability of hybrid automata that may be constructed hierarchically and in a modular way, as is the case in many exemplar systems, be it natural or engineered. Since the basic fundamental step in such constructions is a product operation, which constructs a new product hybrid automaton by combining two simpler component hybrid automata, an essenti...

The behavior of hybrid systems is described by means of continuous and discrete variables. A number of di erent philosophies have been pursued in order to establish a mathematical framework that is able to handle both, continuous and discrete processes. These range from the construction of hybrid automata [1] and structures [2] over the de nition of interfaces between the continuous and the dis...

One of the most important analysis problems of hybrid systems is the reacha-bility problem. State of the art computational tools perform reachability computation for timed automata, multirate automata, and rectangular automata. In this paper, we extend the decidability frontier for classes of linear hybrid systems, which are introduced as hybrid systems with linear vector elds in each discrete ...

We marry continuous time Markov decision processes (CTMDPs) with stochastic timed automata into a model with joint expressive power. This extension is very natural, as the two original models already share exponentially distributed sojourn times in locations. It enriches CTMDPs with timing constraints, or symmetrically, stochastic timed automata with one conscious player. Our model maintains th...

The analysis of hybrid systems exhibiting probabilistic behaviour is notoriously difficult. To enable mechanised analysis of such systems, we extend the reasoning power of arithmetic satisfiability-modulo-theory solving (SMT) by a comprehensive treatment of randomized (a.k.a. stochastic) quantification over discrete variables within the mixed Boolean-arithmetic constraint system. This provides ...